A的平方加B 的平方减4A的平方B的平方等于-----因式分解

因为
a^2+b^2-4a^2b^2
=a^2+b^2-4a^2b^2+2ab-2ab
=(a+b)^2-4a^2b^2-2ab
=(a+b)^2-4a^2b^2-2ab+1/4-1/4
=(a+b)^2-(2ab+1/2)^2+1/4
=(a+b+2ab+1/2)(a+b-2ab-1/2)+1/4
所以
4a^2b^2-(a^2+b^2)
=-(a+b+2ab+1/2)(a+b-2ab-1/2)-1/4
如果原题为(a^2+b^2)^2-4a^2b^2
(a^2+b^2)^2-4a^2b^2
=(a^4+2a^2b^2+b^4)-4a^2b^2
=(a^4-2a^2b^2+b^4)
=(a^2-b^2)^2
=(a-b)^2(a+b)^2